A flush beats a straight because a flush is harder to be dealt. That is the whole rule, and it holds all the way down the list: in five-card poker every category outranks the ones that are easier to make. The order is not arbitrary, and you can rebuild it from a pencil and a few multiplications.
The two hands side by side
Start with what each hand needs. A straight is five cards in rank sequence, such as 5-6-7-8-9, in any mix of suits. A flush is five cards of one suit, in any ranks. Both start from the 1,287 ways to choose five different ranks out of thirteen (that is 13 × 12 × 11 × 10 × 9 divided by 5 × 4 × 3 × 2 × 1).
Ten of those 1,287 rank patterns are sequences, running from ace-low (A-2-3-4-5) to ace-high (10-J-Q-K-A). That leaves 1,277 that are not.
- Straight: 10 sequences, and each card can be any of four suits. That is 45 = 1,024 suit patterns, but 4 of them are all one suit, which makes a straight flush instead. So 10 × 1,020 = 10,200 straights.
- Flush: 1,277 non-sequence rank patterns in each of four suits: 1,277 × 4 = 5,108 flushes. The 10 sequences in a single suit are straight flushes, so they are left out.
The ratio is 10,200 to 5,108, or 1.997 to one. Put another way, five cards dealt at random are about as likely to form a straight as two flushes. Of 2,598,960 possible hands, the flush turns up roughly once every 509 deals and the straight once every 255.
Why the factor is almost exactly two
The two hands ask for different things. A straight asks for a pattern in the ranks and does not care about suits: 1,020 of the 1,024 suit patterns are acceptable. A flush asks for a pattern in the suits, and only 4 of the 1,024 suit patterns will do. But a flush will accept any of 1,277 rank patterns, where a straight will accept only 10.
Compare the two directly. The flush has 1,277 × 4 = 5,108 combinations to the straight's 10 × 1,020 = 10,200. Close to 128 times as many rank patterns, but about 255 times fewer suit patterns, and the two effects nearly cancel to leave a factor of two. The near-miss is a coincidence of a 52-card deck with 13 ranks and 4 suits, not a design.
The full counts for every category are in How rare each five-card poker hand is. This post is about what they mean for the order.
Every rung follows the same rule
Here are the nine standard categories from straight flush down to high card, with the count of hands in each. The royal flush is counted inside the straight flush row.
| Rank | Hand | Hands | Times as common as the hand above |
|---|---|---|---|
| 1 | Straight flush | 40 | - |
| 2 | Four of a kind | 624 | 15.6 |
| 3 | Full house | 3,744 | 6.0 |
| 4 | Flush | 5,108 | 1.36 |
| 5 | Straight | 10,200 | 2.00 |
| 6 | Three of a kind | 54,912 | 5.4 |
| 7 | Two pair | 123,552 | 2.25 |
| 8 | One pair | 1,098,240 | 8.9 |
| 9 | High card | 1,302,540 | 1.19 |
The counts rise at every step, with no exceptions. That is the property that makes the ranking feel fair: if a lower hand were rarer than a higher one, you would have a hand that loses to something you are dealt more often. The sizes of the steps vary a lot, though. The gap between a flush and a full house is small, at 1.36 times, while one pair is nearly nine times as common as two pair.
Checking the claim on a smaller scale
You do not need to trust the big totals. The suit side of the argument can be checked on its own. There are 4 × 1,287 = 5,148 ways to choose five cards of one suit. Of those, 10 per suit are sequences, so 40 are straight flushes, and 5,148 − 40 = 5,108 flushes. The straight side adds up the same way: 10 × 1,024 = 10,240 hands with ranks in sequence, and 10,240 − 40 = 10,200 straights. The 40 straight flushes appear in both lists, which is why they sit at the top of the ranking: they have to be both things at once.
The same logic explains why a straight flush outranks four of a kind, even though 624 is far more than 40. Being in the top row means being the rarest hand, not the most valuable-looking one.
The ranking is a statement about frequency in a standard deck dealt five cards at a time. Change the deck, the hand size or the number of cards you can use, and the order of rarity can change with it. Games that do this usually change the ranking to match.
What the order tells you in play
Two practical points follow. First, a made straight is not a weak holding, just a common one: it is dealt on about 0.39% of hands, against 0.20% for a flush, and both are far rarer than three of a kind at 2.11%. Second, the gap between a full house and a flush is the narrowest in the upper half of the ranking, only 1.36 times, but the order still holds: 3,744 full houses against 5,108 flushes puts the full house on top.
Poker vs Dealer is built on its own five-card rules, and it says plainly that it is not Texas Hold'em. Its in-game rules and payouts screen is where to check exactly how hands are ranked and rewarded there. The maths above is standard five-card poker and describes the rarity of each hand, not the app's rules.
Poker vs Dealer: Offline is five-card poker against the dealer and two computer opponents. Your five cards compete against the house and for the table pot, and you can hold, forge a card by exchanging it, or bail. It plays offline with no account, there are no ads or in-app purchases, and the play-money chips have no cash value.